Connecting curve and plane
If I understood you correctly, You want this :



I would do the following :

Start from your "curved planes gird" :


Make sure every "curved plane" is merged with his neighbors by selecting everything with A → open the "Specials" menu with W and clicking "Remove Doubles".


Then, hold Alt and click on an border edge of the "gird" in order to select the whole contour :


Extrude down this edge loop by pressing E and Z to constraint the extrusion on the Z axis. Click to confirm the action.

Make the extruded loop perfectly plane via a "zero scale" on z-axis: S + Z + Numpad 0 and click to confirm.

Then fill the bottom face, either via F, or via CtrlF → Gird Fill which may allow you to make a correct topology.



In addition, I would make a shade smooth, then turn on the "Auto Smooth" in the Object Data area :


This will make the whole object look smooth while keeping the sharp edges like they're supposed to look like.